/** Let's generate "words" from a set of strings that's recursively defined 
 *  by this grammar:
 *  S --> AB
 *  A --> ""
 *  A --> aA
 *  B --> "" 
 *  B --> aBb
 *  First, try to figure out what A and B represent.  Then this will tell
 *  you about the entire set S.  How would you describe this "language" ?
 */
public class Generate
{
  public static void main(String [] args)
  {
    // Generate 10 words.
    for (int i = 0; i < 10; ++i)
    {
      String S = A() + B();
      System.out.println(S);
    }
  }

  // This recursive function will either pick the rule "" or the rule aA.
  // Since nextDouble() returns a number between 0 and 1, if we compare
  // it to 0.3, then we have a 30% chance of returning the base case.
  public static String A()
  {
    if (Math.random() < .3)
      return "";
    else
      return "a" + A();
  }

  // B is similar to A, but this time, we also concatenate a 'b' after
  // returning from recursion.
  public static String B()
  {
    if (Math.random() < .3)
      return "";
    else
      return "a" + B() + "b";
  }
}

/*===============================================
Example output:
-------------------------------------------------
aaaaaaaaaaaaabbbbbbbbbb
aab
a
aaaaabbb
aaaabb

ab
aa
aaaabbb
aaaaaabbbbbb
=================================================*/